The scene: The Buckhorn Exchange is Denver's oldest restaurant, but more importantly it is the most atmospheric in the city – and maybe the country. The standalone brick building is a survivor in the much-changed Santa Fe neighborhood, now undergoing another renaissance, with a light-rail station just steps from the eatery, making it ultra-accessible. The place oozes saloon ambiance, down to the swinging doors that guard the bathrooms. The interior is all dark heavy wood, high pressed-tin ceilings, red-and-white checkered tablecloths, and menus printed like Old West newspapers. But it is the artifacts and decor that define the place. The restaurant is home to more than 500 mounted animals and trophy heads of every description, including bears, birds, mountain lions, elk, rattlesnakes and even Rocky Mountain non sequiturs like a monkey and African Cape Buffalo – shot by President Teddy Roosevelt, no less.

There are also more than 200 antique weapons displayed in equally vintage glass cases throughout, photos of famous patrons (Bob Hope, Jimmy Cagney, Charlton Heston, Roy Rogers), and just odd stuff everywhere you look. The restaurant was the regular watering hole of Buffalo Bill Cody, whose likeness is prominently displayed, and the stuffed golden eagle over the front booth was a gift from his friend Chief Sitting Bull, who also ate here. Buffalo Bill's regular drink was a "Stone Fence," half bourbon and half apple juice, and you can try one here today. If you have any interest in Western history, this restaurant-cum-museum is not to be missed, and it is a regular occurrence for patrons to stroll around taking pictures and examining the endless items.

Downstairs is broken up into a couple of dining areas, separated mainly by display cases, and upstairs is a period bar, hand-carved in Germany in the 1850s from white oak, complete with antique brass cash register. This anchors a lounge where live cowboy music is performed several nights each week by a duo on autoharp and guitar who have been at it for three decades. A more recent change is the extension of the second floor into an open-air roof garden.

The Buckhorn Exchange proudly displays Colorado liquor license No. 1, and is firmly rooted in its traditions, but one nod to modernity is the endless array of framed articles and reviews from newspapers and magazines around the world which line the staircase and entryway. It has also been the subject of shows like Bizarre Food and Man vs. Food. American cowboy culture is immensely popular in Japan and Germany, and customers seek out the place to the extent that the menu includes both languages. Several presidents, from Roosevelt to Carter to Reagan have dined here – JFK was a famously big tipper - along with foreign heads of state, astronauts and royalty. They come for the animals on the wall and the animals on the plate, in many cases the same unusual species.

The food: Ostensibly a steakhouse, the experience at Buckhorn Exchange is much more about eating the signature and often unusual game dishes. "As great as our steak is, you can have steak as good or better in many other cities, but there aren't too many places where you can order buffalo prime rib," says Bill Dutton, partner and general manager. Even in bison–mad Colorado, burgers and steaks are the norm, and I have never seen prime rib anywhere else. "They came for the buffalo in 1893, and they still come for it today."

To make the game-centric menu as user-friendly as possible, many combination plates are offered, such as elk and quail, and oddly, the single most popular dish is not even on the menu. Years ago they offered an elk and buffalo combo plate, and it was a runaway hit, but because they occasionally run out of their supply of farmed elk (everything but the rattlesnake is farmed), they don't print it, and instead run it as a "special" – every night. In addition, just about every protein offered as a dinner plate is also available a la carte so you can customize combos, such as a buffalo rib steak dinner with quail on the side, or elk with duck. Where else would you ever have the chance to order "a yak steak on the side," another recurring special, raised in Montrose, Colo.?

The other signature dish, and nearly as hard to find as yak, is the Rocky Mountain oysters, a nice way of saying bulls' testicles. Here they are sliced into disks, seasoned and batter-fried, and while they may sound off-putting, they are actually quite good, tasting not like chicken, but rather like fried calamari. I expected to eat one for research purposes and possibly have nightmares afterwards, and my dining partners were equally unconvinced, but we were all pleasantly surprised and the entire plate quickly vanished. If you like fried finger food, it is hard not to like these, which are chewy but not too chewy, meaty but with a slightly seafood-esque taste, and served with a trio of excellent dipping sauces: spicy mustard, horseradish peppercorn and cocktail.

There are several other unique appetizers, which also makes it easy to share and try many different unusual offerings during a visit here. Fried alligator tail, in small chunks, is fine for the novelty but doesn't have much flavor – white meat but not quite like chicken. On the other hand, the rattlesnake-topped queso dip with chips was quite good. There is also a buffalo sausage and medley of beef, buffalo and elk sirloin tips in a sauce of the day.

All main courses are served with salad or soup, and one side from a choice of wild rice blend, house-made kettle chips, baked beans and baked or mashed potatoes. The standard soup is a nearly forgotten classic, Navy bean, while the salad comes with the house signature buttermilk dressing and mandarin orange slices, another old-school touch. The bestsellers among main courses are the less common buffalo, elk and quail. Less exciting mainstays include "The Big Steak," 1 1/2 to 3 1/2 half pounds for two to five guests to share, plus salmon, Colorado lamb and Cornish game hens.

Some of the meats, such as the duck, are merely okay. The elk is leaner and sweeter than beef, has just a hint of gaminess, not nearly as strong as venison, but not that much flavor. The yak was surprisingly tender and almost pork-like. The quail was quite good and the dry-aged buffalo steak better than the other game steak cuts. But the big winner was the buffalo prime rib, less juicy and more concentrated than the standard beef version, really meaty and delicious. In general, while the proteins are exotic, the sides and presentations are pretty basic, and with exceptions like the prime rib and Rocky Mountain oysters, nothing was stunning (except the crazy good hot Dutch apple pie). But it is impossible to separate the food from its rarity and from the absolutely incomparable setting. Taken as a whole, the Buckhorn Exchange is simply a must-visit, and I'd gladly go again anytime.

What regulars say: "Denver has a lot of great restaurants now, but so do New York, L.A. and other cities. But no one has anything like the Buckhorn Exchange, it's like going back in time," says Alex Weiner, an educator who was revisiting his Colorado ski bum days on a recent visit.

Pilgrimage-worthy?: Yes – one-of-a-kind history plus a one-of-a-kind menu make it completely unique.

Larry Olmsted has been writing about food and travel for more than 15 years. An avid eater and cook, he has attended cooking classes in Italy, judged a barbecue contest and once dined with Julia Child. Follow him on Twitter, @TravelFoodGuy, and if there's a unique American eatery you think he should visit, send him an e-mail at travel@usatoday.com. Some of the venues reviewed by this column provided complimentary services.